Complex angular momentum

David R. Masson

H. M. Nussenzveig

Vladimir S Popov, E.I. Dolinsky

Ducharme, Robert J.

The quantum mechanical operator for angular momentum is transformed from the real plane into the complex plane. In doing so, the Cauchy-Riemann (C-R) equations are interpreted as constraint conditions defining two distinct domains where complex differentiation is permitted. It is shown each of these domains contains an orbital angular momentum contribution plus an non-orbital term that cancels out between them. It is further shown the field equations for spinning quantum particles include C-R equations that restrict the particles to a single complex constraint space. It is therefore proposed the non-orbital term in the constraint space angular momentum is the source of the spin.

A. J. van Wonderen, K. Lendi

The standard representation of angular momentum on Bargmann's Hilbert space of analytic functions is extended such that domains of operators include non-analytic functions, which are square integrable. Generalized eigenfunctions of angular momentum are proposed, which contain arbitrary complex constants. The eigenfunctions are shown to satisfy a basic requirement which follows from group theory.

Kundeti Muralidhar

A charged elementary particle fluctuates from its mean position because of the presence of zero-point fields in vacuum. Considering the complex oscillations of the particle as two general types of rotations, an attempt has been made to explore the classical origin of spin angular momentum. The oscillations of the particle in zero-point field can be transformed as rotations on complex plane and the spin angular momentum is identified with imaginary part of rotations. The quantum value of spin angular momentum has been determined within the purview of stochastic electrodynamics. Keywords: Spin angular momentum, Zero-point energy, Stochastic Electrodynamics. 1.